https://file.aiquickdraw.com/mathbot/file/1727577925339ozkfc0ng.jpg

I see you've uploaded a math problem about bearings. Here's the breakdown of the problem from the image:

### Problem description:
There are three fishing boats: K, L, and M. The diagram shows their relative positions. 
- K is on a bearing of 040° from L.
- M is directly south of L.
- Distances given are:
  - \( LM = 120 \, \text{km} \)
  - \( KL = 80 \, \text{km} \)

The tasks are:
1. To indicate the bearing of 040° on the diagram.
2. To calculate the angle \( \angle LKM \).

### Work on the tasks:

#### (ii) **Show the bearing of 040° on the diagram:**
The bearing of 040° means that the angle measured clockwise from the north line at L to the line joining L and K is 40°. The diagram already labels this as 40°, so this step is already shown.

#### (iii) **Calculate the measure of \( \angle LKM \):**
- Since \( M \) is directly south of \( L \), the line \( LM \) forms a vertical line with the north direction.
- \( \angle LKM \) is the exterior angle formed between \( LM \) and \( LK \).

To calculate \( \angle LKM \):
- We know that the straight-line angle at L (the angle between north and south) is 180°.
- The bearing angle between north and the line \( LK \) is 40°.
- Thus, \( \angle LKM = 180° - 40° = 140° \).

This calculation seems correct based on the diagram and given information.

Would you like further clarification or more details on any part of this problem?

### Additional Questions:
1. How do bearings relate to standard angular measurements?
2. What other properties can be calculated with this triangle (e.g., distances)?
3. Can the Law of Cosines be used for further calculations in this scenario?
4. How would this problem change if M was not directly south of L?
5. How can bearings be useful in real-world navigation?

#### Tip:
Always ensure that bearings are measured clockwise from the north direction, and that angles in triangles sum up to 180°.

The diagram shows the relative positions of three fishing boats K, L, and M. K is on a bearing of 040° from L, and M is due south of L. Distances LM = 120 km and KL = 80 km. Tasks include: (ii) showing the bearing of 040° on the diagram, and (iii) calculating the measure of angle LKM.

Solve a bearings problem involving three fishing boats positioned at K, L, and M. Calculate the angle LKM given bearings and distances. Suitable for students in Grades 9-11, this problem teaches how to apply bearings, straight-line angles, and the Exterior Angle Theorem.

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